Saturation and forced volume magnetostriction of Fe-rich FeZr amorphous alloys

AC susceptibility, saturation and forced volume magnetostriction were studied on iron-rich zirconium amorphous alloys a-Fe_100-xZr_x (8 at% ≤ x ≤ 12 at%). The experimental results are discussed in relation to the re-entrant spin glass state. It is found that the transverse magnetostriction accompanies a remarkable magnetic aftereffect in the spin glass phase, and that the forced volume magnetostriction shows an apparent peak at the ferromagnet to spin glass transition where the ac susceptibility has a cusp.     

Spin and energy coupling in the Ising model with a transverse field: One dimension,T=∞

The dynamics of the one dimensional Ising model with a transverse field is studied in the limit T = ∞. Numerical studies of the classical chain and exact calculations for the spin $\text{1}\text{2}$ chain indicate the presence of an energy density term in the dynamic spin susceptibility along the direction of the field.     

The zero field Kondo susceptibility at lower temperatures

The zero field impurity spin susceptibility is calculated for spin $\text{1}\text{2}$ Kondo systems. By taking into account the self energy of the transverse impurity spin excitations the previous selfconsistent approximation is modified such that the unitarity bound for spin wave scattering is taken care of. For lower temperatures an improvement for the static susceptibility is achieved.     

Theory and calculations for a spin glass

We obtain the properties of a mean-field spin-glass (in which the bonds connecting each spin to every other spin are “frozen-in” with random signs), by locating the zeros of the partition function in the complex T plane. For N = 5 and 9 spins, we obtain the relevant polynomials and zeros explicitly, and the resulting thermodynamic properties (free energy, specific heat, magnetic susceptibility, etc.). We then analyze the properties of such a system in the thermodynamic limit N → ∞, where it is impossible to obtain the polynomials directly but where the presumed location of the zeros can be usefully construed. In this limit, the thermodynamic functions are obtainable as functions of the distribution functions of monopoles, quadrupoles, and possibly higher-order poles.     

Transverse susceptibilities of ferromagnetic spin wave interacting with phonon reservoir, II: Temperature dependence of line shapes

A form of the transverse magnetic susceptibility of a ferromagnetic spin system with a uniaxial anisotropy energy and an anisotropic exchange interaction, interacting with a phonon reservoir, is derived in the spin-wave approximation using the TCLE method, where the phonon reservoir interacts with not only the x and y components of each spin but also its z component. The transverse magnetic susceptibility is numerically and analytically studied for the system of one-dimensional infinite spins in the lowest spin-wave approximation, by assuming a damped oscillator model of the phonon reservoir. The temperature dependence and wave number dependence of the susceptibility are numerically investigated for the half-widths and peak-heights of the line shapes in the resonance region. It is shown that as the temperature increases, the half-widths of the line shapes increase and the peak heights decrease in the resonance region, and that as the wave number increases, the half-widths of the line shapes decrease and the peak heights increase in the resonance region. It is also shown that as the uniaxial anisotropy energy of the z direction increases or as the exchange interaction between the z components of spins increases, the half-widths of the line shapes decrease and the peak heights increase in the resonance region. It is besides shown that as the characteristic frequency of the phonon increases, the line shapes show ‘motional broadening’ at the low temperature and show ‘motional narrowing’ at the high temperature. Furthermore, the resonance frequency is shown to increase as the wave number increases or as the temperature increases. The numerical results are examined analytically.     

Spin wave excitations in amorphous itinerant ferromagnets II. Dynamical susceptibility

The Izuyama, Kim, and Kubo theory of dynamical susceptibility in crystalline itinerant ferromagnets is extended to the amorphous itinerant ferromagnets. Effects of amorphousness in spin wave spectrum, given by the poles of the susceptibility, is discussed.     

Dynamical susceptibility of the ising model in a transverse magnetic field

An approximate expression is obtained for the dynamical susceptibility, χ_zz(q, ω), of the spin one half, simple cubic Ising model in a transverse magnetic field, which is appropriate to the disordered state (〈S_z〉 = 0). The susceptibility along the direction of the field is shown to contain a thermal part with a relative weight proportional to the difference between the isothermal and adiabatic susceptibilities and a width determined by the thermal diffusion constant.     

The peculiarities of coupled electromagnetic and magnetoelastic waves in antiferromagnets

A spectrum of coupled electromagnetic, spin and elastic waves in a two-sublattice antiferromagnet with weak ferromagnetism is theoretically investigated. The influence of the g-factor anisotropy and the transverse and longitudinal relaxation in magnetic subsystem on the spectrum of coupled waves is considered. The most changes of dispersion laws occurred in long-wavelength approximation and near the spin reorientation point, then the vectors of ferromagnetism and antiferromagnetism reoriented onto another crystallographic axis. It is shown that the magnetoelastic, the Dzyaloshinsky and the dipole interactions, the anisotropy of g-factor, the external magnetic field and the longitudinal susceptibility determine the activation of quasiferromagnetic waves. The dispersion laws of quasielectromagnetic and quasielastic waves can change from linear dependence to square. At large damping in magnetic subsystem, one from these modes can become the pure relaxation one.     

COMPASS and HERMES contributions to our understanding of the nucleon spin

An update is given on the ongoing experimental investigation of the spin structure of the nucleon, with particular emphasis on the results from the COMPASS and HERMES experiments. Both longitudinal and transverse spin phenomena are covered. In the first case, the hot topic is the direct measurement of the gluon polarization. Evidence is presented for ΔG/G being small around x_g?0.1, and the first moment of ΔG should not be larger than 0.2-0.3. About transverse spin effects, evidence is given for new phenomena, associated with transverse-momentum-dependent distribution and fragmentation functions, which might explain the transverse spin phenomena observed for a long time in pp scattering.     

Study of the Hanle effect with the transverse component of the electron spin orientation in III–V semiconductors

The Hanle effect in n-GaAs and p-AlGaAs is studied in the longitudinal and transverse geometries of the experiment, in which the emission is recorded parallel and perpendicular to the spin direction of optically oriented electrons, respectively. The factors responsible for the error in determining the sign of the electron g factor in GaAs studied in the transverse geometry of the experiment are considered. It is shown that the results obtained from measurements of the transverse spin component of the orientation are useful in determining the parameters of semiconductor structures.     

On the magnitude of the local moment in the Anderson model

Consideration of the self-consistent coupling between transverse spin fluctuations and charge fluctuations at the impurity provides an understanding of the magnetic atom's susceptibility law which reduces to that appropriate for a spin one half only in the symmetric configuration at low temperatures.     

Dynamics of spin fluctuations in the Heisenberg paramagnet

The lowest-energy poles of the dynamic spin propagator for the Heisenberg model at T ? T_c are estimated using a gaussian approximation for the second-order memory function. The poles are connected with the observed maxima of the neutron scattering function at large momentum transfer.     

Nonlinear static susceptibility of the Ising spin glass in chaotic and transverse fields

The static volume (linear and nonlinear cubic) magnetic susceptibility is calculated for the Ising spin glass in random longitudinal and transverse magnetic fields. The phase transition from the paramagnetic state to the spin glass state is investigated. Divergence of the nonlinear susceptibility indicative of the phase transition is established. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 3–6, October, 2005.     

Transverse spin structure of hadrons from lattice QCD

This paper presents recent lattice QCD calculations of transverse spin densities of quarks in hadrons.² Based on our simulation results for the tensor generalized form factors, we find substantial correlations between spin and coordinate degrees of freedom in the nucleon and the pion. They lead to strongly distorted transverse spin densities of quarks in the nucleon and a surprisingly non-trivial transverse spin structure of the pion. Following recent arguments by Burkardt [M. Burkardt, Phys. Rev. D 72 (2005) 094020], our results imply that the Boer-Mulders function , describing correlations of the transverse spin and intrinsic transverse momentum of quarks, is large and negative for up-quarks in the proton and the π⁺. This supports the recent hypothesis that all Boer-Mulders functions are alike [arXiv:0705.1573], and also provides additional motivation for future studies of azimuthal asymmetries in πp Drell-Yan production at, e.g., COMPASS.     

The effects of electron–phonon interaction on anisotropic RKKY interaction in graphene nanoribbon

We study the Ruderman–Kittle–Kasuya–Yosida (RKKY) interaction in doped armchair graphene nanoribbon. The effects of both external magnetic field and electron-Holstein phonon on RKKY interaction have been addressed. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a magnetic field along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain both transverse and longitudinal static spin susceptibilities of armchair graphene nanoribbon in the presence of electron-phonon coupling and magnetic field. The spin susceptibility components are calculated using the spin dependent Green’s function approach for Holstein model Hamiltonian. The effects of spin polarization on the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the influences of magnetic field on the spatial behavior of in-plane and longitudinal RKKY interactions are different in the presence of magnetic field.     

A Compensation Temperature Induced by Transverse Fields in a Mixed Spin-1 and Spin-3/2 Ising Ferrimagnetic System

A mean-field theory is developed for a mixed Ising ferrimagnetic system consisting of spin 1 and spin 3/2 with different transverse fields. The phase diagram and the thermal behaviour of magnetizations are studied. We find that a compensation point induced by different transverse fields can be observed, although the system never exhibits any compensation point for either zero or uniform transverse fields. The anomalous behaviour of the initial longitudinal magnetic susceptibility in the vicinity of the compensation and critical temperatures is also obtained.     

Quantum HeisenbergS=1/2 spin glass with ferromagnetic coupling and random Dzyaloshinskii-Moriya interactions

By means of the generalized static replica symmetric spin glass theory, a quantum HeisenbergS=1/2 spin glass model with the infinite-ranged random Dzyaloshinskii-Moriya (DM) interaction and ferromagnetic coupling is investigated. The dependence of entropy, specific heat, susceptibility and the corresponding order parameters on temperature is studied numerically for different ferromagnetic interactions and fixed anisotropy. Two spin glass phases has been found including transverse and mixed spin glass phases. It has been shown that the local susceptibility exhibits double-cusp features for different ferromagnetic coupling (J ₀). Phase transition poins are found in the specific heat-temperature plane at various ferromagnetic coupling values. Additionally, the dependence of the spontaneous moment on temperature is calculated.     

Effect of spin diffusion on the spin resonance in local moment systems

The effect of conduction electron spin diffusion on linewidth, lineshift and residue of the spin resonance in local moment systems is investigated. For the calculation of the transverse susceptibility a previously established kinetic equation approach is used. Low temperature Kondo-type anomalies of spin relaxation and diffusion are taken into account in the framework of Suhl's theory. The susceptibility exhibits considerable structure as a function of wavevector. In particular it is shown that the magnetic resonance bottleneck is broken for sufficiently large wavevectors. The effect of relaxation proceeding to local instead of total equilibrium is investigated and shown to introduce only minor modifications with one possible exception. Application of the theory to transmission electron spin resonance (TESR) is also discussed.     

Low temperature nonequilibrium dynamics in transverse Ising spin glass

The real part of the time-dependent ac susceptibility of the short-range Ising spin glass in a transverse field has been investigated at very low temperatures. We have used the quantum linear response theory and domain coarsening ideas of quantum droplet scaling theory. It is found that after a temperature quench to a temperature T ₁ (lower than the spin glass transition temperature T _g ) the ac susceptibility decreases with time approximately in a logarithmic way as the system tends to the equilibrium. It is shown that the transverse field of tunneling has unessential effect on the nonequilibrium dynamical properties of the magnetic droplet system. The role of quantum fluctuations in the behavior of the ac susceptibility is discussed.Received: 26 February 2004, Published online: 18 June 2004PACS: 75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.) - 75.10.Nr Spin-glass and other random models - 75.50.Lk Spin glasses and other random magnets     

Magnetic susceptibility of MnZn and NiZn soft ferrites using Laplace transform and the Routh-Hurwitz criterion

This paper is devoted to study the Routh-Hurwitz stability criterion from the MnZn and NiZn soft ferrites using a phenomenological model with the gyromagnetic spin contribution and domain wall contribution. The magnetodynamic equation and the harmonic oscillator equation have been used to obtain the domain walls and the spin contribution of the magnetic susceptibility. The ferrite materials have been considered as linear, time invariant, isotropic and homogeneous, and the magnetization vector is proportional to the magnetic field vector. The resulting expression of the magnetization in time domain of both ferrites under study has been obtained by mean of the inverse Laplace transformation applying the residue method. The poles of the magnetic susceptibility have negative real parts, which ensures that the response decays exponentially to zero as the time increase. The degree of the numerator's polynomial of the magnetic susceptibility is less than the degree of denominator's polynomial in the magnetic susceptibility function: and the poles are located in the half left s-plane. Then the system is bounded-input, bounded-output (BIBO), and the results agree with the Routh-Hurwitz stability criterion for the MnZn and NiZn soft ferrites.